Theorem necon1biOLD 2049

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon1bi.1	|- (A =/= B -> ph)

Assertion

Ref	Expression
necon1biOLD	|- (-. ph -> A = B)

Proof of Theorem necon1biOLD

Step	Hyp	Ref	Expression
1		df-ne 2019	. . 3 |- (A =/= B <-> -. A = B)
2		necon1bi.1	. . 3 |- (A =/= B -> ph)
3	1, 2	sylbir 218	. 2 |- (-. A = B -> ph)
4	3	con1i 112	1 |- (-. ph -> A = B)

Syntax hints:  -. wn 2   -> wi 3   = wceq 1298   =/= wne 2017

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-ne 2019

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